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Proof step 21 from proof replay-cons-add-orphan (previous step)

log-cons(log, fs), replay-safe(log, fs, fi ⊖ fo), datakey(m, m0) ∈ ri ⊦ (ri ⊖ (ro ++ inodekey(ino)))[datakey(m, m0)] = ((ri ⊖ inodekey(ino)) ⊖ ro)[datakey(m, m0)], m = ino, datakey(m, m0) ∈ ro, inodekey(m) ∈ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: at-dels-ro-data seq: ⊦ datakey(ino, n) ∈ ri ∧ ¬ datakey(ino, n) ∈ ks ∧ ¬ inodekey(ino) ∈ ks → (ri ⊖ ks)[datakey(ino, n)] = ri[datakey(ino, n)] subst: [n, ino, ks, ri] → [m0, m, ro ++ inodekey(ino), ri] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ks → (key ∈ ks ++ key0 ↔ key = key0); (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s) Used terms: m0, m, ro ++ inodekey(ino), ri